10.2.5 Discretization

Many of the numerical peculiarities can be traced back to the fact that there is no ``good'' discrete Wigner transform as explained in Section 8.2. Some are minor technical issues, which can be solved by increased implementation efforts. However, often simulations still use the simple ``standard discretization'' (i.e., first order upwinding with Frensley's completeness condition for the mesh) and hazard the consequences. A good reference where discretizations of the Wigner function method are compared is Biegel's PhD thesis [Bie97]. In contrast for the QTBM the choice of discretization was a non-issue.